Question

19. A muonic hydrogen atom consists of a muon (m=106 MeV/c²) in place of an electron. At what state (n) does the radius reach to 2nm? (fm = $10^{-15}$m) a. 84 b. 26 c. 49 d. 42 e. 59 $\mu = \frac{m_p m_m}{m_p + m_m} \approx 95 \frac{MeV}{c^2}$ $r_m = \frac{\hbar^2}{hc^2 \mu} = 2.8E-4 nm = a_0$ $2nm = r = n^2 a_0$ $\sqrt{\frac{2nm}{a_0}} = n = 84.062$ $n \approx 84$

Name: 19 a muonic hydrogen atom consists of a muon m106 mevc2 in place of an electron at what state n does the radius reach to 2nm fm 10 15m a 84 b 26 c 49 d 42 e 59 mu fracmp mmmp mm approx 9 97636
Uploaded: 2023-05-11T16:30:55-08:00
Channel: Ankur S
Description: 19 a muonic hydrogen atom consists of a muon m106 mevc2 in place of an electron at what state n does the radius reach to 2nm fm 10 15m a 84 b 26 c 49 d 42 e 59 mu fracmp mmmp mm approx 9 97636

          19. A muonic hydrogen atom consists of a muon (m=106 MeV/c²) in place of an electron. At what state (n) does the radius reach to 2nm? (fm = $10^{-15}$m)
a. 84
b. 26
c. 49
d. 42
e. 59
$\mu = \frac{m_p m_m}{m_p + m_m} \approx 95 \frac{MeV}{c^2}$
$r_m = \frac{\hbar^2}{hc^2 \mu} = 2.8E-4 nm = a_0$
$2nm = r = n^2 a_0$
$\sqrt{\frac{2nm}{a_0}} = n = 84.062$
$n \approx 84$

$19 a muonic hydrogen atom consists of a muon m106 mevc2 in place of an electron at what state n does the radius reach to 2nm fm 10 15m a 84 b 26 c 49 d 42 e 59 mu fracmp mmmp mm approx 9 97636$

Added by David B.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Ankur S

05/11/2023

Step 1

The reduced mass ($\mu$) is given by: $\mu = \frac{m_p m_m}{m_p + m_m}$ where $m_p$ is the mass of the proton and $m_m$ is the mass of the muon. The problem provides $m_m = 106 MeV/c^2$. The mass of the proton is approximately 938 MeV/c². Therefore: $\mu Show more…

Show all steps

Thanks for your feedback!

19. A muonic hydrogen atom consists of a muon (m=106 MeV/c²) in place of an electron. At what state (n) does the radius reach to 2nm? (fm = $10^{-15}$m) a. 84 b. 26 c. 49 d. 42 e. 59 $\mu = \frac{m_p m_m}{m_p + m_m} \approx 95 \frac{MeV}{c^2}$ $r_m = \frac{\hbar^2}{hc^2 \mu} = 2.8E-4 nm = a_0$ $2nm = r = n^2 a_0$ $\sqrt{\frac{2nm}{a_0}} = n = 84.062$ $n \approx 84$